Note: This review represents the topics covered by the final exam. It is in no way intended to represent the quantity of any particular type of problem on the final exam. The answers and graph paper are provided at the end of this packet. Terminology: Be able to recognize, identify and use these terms. Absolute value Equation Factor Multiple LCD Reciprocal Solution All real numbers Conditional Contradiction Identity Set-builder notation Inequality Interval notation Roster notation x-intercept y-intercept Origin Quadrant Ordered pair Slope Slope-intercept form Parallel lines Perpendicular lines Linear system System of linear inequalities Consistent system Inconsistent system Independent equations Dependent equations For problems 0, simplify the expression. You could use a calculator, but it s best to have an understanding of order of operations (and fraction operations) without a calculator.. 5 ( ) ( 6). ( )( ) 7 ( 0) 7.. + 9 6 8 9 5 5 6. ( ) ( ). 7 6 +. +. 5 7 7 9 0 0 5 9 5. 5 5. ( 5 + ) 5 + ( ) 6. ( ) 5 + 5 + ( ) 5 7 + 7. ( + ) 6. 5 5 6 6 7. 8. 6 5 0 5 0 5 75 9 6 8. + ( ) 9. 9 0. + 9 9. 6 ( ) ( 8) 7 86 { + ( ) } 0. + 5 5 0
For problems, set up and solve a linear equation to determine the solution.. What number is 50% of 7?. Write 0.05% as a decimal.. What is 6 increased by 0%? 5. Write 0 as a percent.. What percent of 70 is? 6. Write 0 as a percent. For problems 7 5, set up the linear equation to solve. Be sure to define the variable used in your equation. 7. A pipe feet long is cut into three pieces. The first piece is twice as long as the second piece and the third piece is 6 feet longer than the second piece. What are the lengths of all pieces? 8. One number is times a second number and their sum is 0. Find the numbers. 9. A major league pitcher throws a ball upward with an initial rate of 0 feet per second. The height h (in feet) of the ball after t seconds is given by the formula h= 0t 6t. Determine the height of the ball after seconds. 0. In a physics class of 6 students, 5 more students received B s than A s and twice as many students received C s as A s. Seven people received a grade below C. How many students received A s, B s and C s?. Food for hummingbirds must contain four times as much water as sugar. How much sugar and water are needed to make 0 cups of food?. An employer announced a 6 ½ % salary increase for full-time employees. What was the employee s previous salary if their salary increased to $8,95?. One angle of a triangle is 0 degrees less than another angle, and the third angle is 0 degrees less than twice the first angle. Find the measures of the three angles.. Two teachers are team-teaching for the first time together at Null Elementary School. They are planning on shopping together to purchase decorations for their new room. They are told that they will teach in one large room with a perimeter of 8 ft and the length is 6 ft greater than twice its width. What are the dimensions of their classroom? 5. A plumbing company charges $5 for the service call plus $5 for each hour of work. The owner of an apartment complex budgeted $00 to repair its oven. How many hours of service can the owner afford so that she does not exceed her budget?
For problems 6-9, determine the slope of the line that passes through the given points. You may use the graph paper provided if needed. 6. (, ) and (, 5) 8. (, 0 ) and ( 5,6) 7. (, 5 ) and (, 5) 9. (, ) and (, 5) 0. Determine the slope of the lines in the graphs below. a) b) For problems -, use the given graph to answer the questions that follow.. Approximate the value of x when y =.. Write the x-intercept as an ordered pair.. Write the y-intercept as an ordered pair.. Write the equation of the line in slope-intercept form.
For problems 5-8, graph the line and determine the slope and intercepts. You may use the graph paper provided. 5. x y = 7. 5 x + = 6. x+ 5y = 0 8. y = 9. Find the equation of the line that passes through the points (, ) and (, ) 50. Find the equation of the line with slope that passes through (0,). 5. Find the equation of the line with slope that passes through (, ). 5. Find the equation of the line that passes through (, ) and (,). 5. Find the equation of the line with slope 0 that passes through (, ). 5. Find the equation of the line that is perpendicular to y = x 5 and passes through 0, 5. 55. Find the equation of the line parallel to x + y = that passes through (, ). 56. Find the equation of the line perpendicular to x = and passes through (, 7). For problems 57-60, sketch the solution on a number line, and write the solution in set-builder and interval notation. 57. Illustrate the solution set of x 6> 0. 59. Illustrate the solution set of 0 x 58. Illustrate the solution set of 6 x 60. Illustrate the solution set of 5 ( x ) x+ Solve the following inequalities. Write your answer in interval notation. 6. 8x + 8 or x 5< 7 6. 8x + 8 and x 5< 7
Solve the following systems of equations. 6. x y = 7 x+ y = 9 What is the y-coordinate of the solution? 65. 5x y = 8x+ 6y = 0 What is the y-coordinate of the solution? 6. y+ x= 7 x+ 6y = What is the x-coordinate of the solution? For problems 66 and 67, solve the system of equations graphically. You may use the graph paper provided. 66. 67. x y = 5 5x y = x 7y =.5x.5y = 7.5 Graph the following system of inequalities. You may use the graph paper provided. 68. x+ y x+ y 0 70. x+ y x y< 69. x y > 7. x+ y > 5x y >7 Set up and solve a linear system to determine the solution to the application problems. Be sure to define your variables used in the linear system. 7. Jack has saved a total of $.5 in nickels and dimes in his piggy bank. He has 0 more nickels than dimes. How many of each denomination does he have in his piggy bank? 7. The perimeter of a desk is 8 feet. If the width is feet less than the length, find the dimensions of the desk. 7. Del Monte Bloom Energy Drink contains 50% fruit juice while Rockstar Juice, an energy/ juice hybrid, contains 70% fruit juice. How much of the Del Monte Bloom Energy Drink should be mixed with the Rockstar Juice drink to make ounces of a 65% fruit juice blend? 75. Corey has just moved into his first apartment and is trying to decide between two different calling plans so that he can use his phone. The Unlimited Plus Plan has a $.99 monthly fee with unlimited free long-distance calls. The One Rate 0 Nationwide Direct Plan has a monthly fee of only $.99, but there is also a 0 charge for each call made. How many calls would someone with the One Rate 0 Nationwide Direct Plan have to make for the monthly cost to be the same as the Unlimited Plus Plan? 5
76. Evaluate: 5 0 ( ) 77. Replace? with the correct symbol: > < = 5? 5 Introductory Algebra Final Exam Review 78. The sum of two supplementary angles is80. If the larger angle is 0 more than 7 times the smaller angle, find the measure of the larger angle. 79. Anita recently received a 7.8% pay cut. Her hourly wage is now $.. Find her hourly wage before the pay cut. 80. Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at 7 miles per hour and Dave bikes at 0 miles per hour. How long will it be until they are 7 miles apart from each other? 8. Two trains leave a train station at the same time. One travels north at 9 miles per hour. The other train travels south at miles per hour. In how many hours will the two trains be miles apart? 8. If a plane can cover 906 miles in hours, how long will a 06 mile trip take? 8. A plane can travel 980 miles in 9 hours with a tailwind. On the return trip, the trip takes hours. Find the speed of the plane in still air. 8. A ski lift runs at a rate of ft/sec. At that rate, how many minutes would it take to cover a mile? (hint: mile = 580 feet) 85. The perimeter of an equilateral triangle is 7 inches longer than the length of one side. Find the length of one side. 86. Find the measure of each angle of the triangle. The second angle is more than twice the first angle and the third angle is less than times the first angle. 6
ANSWERS. 7. 76 8. 8 55. y = x... 0 5. 6. 7. 7 5 8. 9. 0.... 7 7 7 9 7 6. 9 0 5. 6. 50 7 8. 9. 0. 7 5 89 9 00. 85. 7.. 0 %. 0.0005 5. 000 % 6. 0 % 7. ft, 9 ft, 0 ft 8. ; 96 9. 6 ft 0. A: 6; B: ; C:. cups sugar; 6 cups water. $6,7.8. 55º, 5º, 80º. 6 ft by 78 ft 5. 6.6 hours 6. 8 7. 0 9. undefined 0. a).. (0, ). (, 0). y = x+ b) undefined Graphs for #5 8 are attached. 5. 6. m = ; (,0); (0, ) m = ; ( 5,0); (0, ) 5 7. m is undefined; (8, 0) ; no y-intercept 8. m = 0; (0, ) ; no x-intercept 9. x = 50. 5. 5. y = x+ y = x+ 7 y = x+ 5. y = 5. y = x+ 5 56. y = 7 Number lines for #57 60 are attached. 57. { xx> } ; (, ) 58. { xx } ; (, ] 59. { xx 5} ; (, 5] 60. xx 6. (, ) 6. [,6 ) 6. 7 6. 5 65. ;, Graphs for #66 and 67 are attached. 66. (,) 67. no solution Graphs for #68 7 are attached. 7. dimes, nickels 7. 8 ft by 6 ft 7. oz Del Monte; 9 oz Rockstar 75. 00 calls 7
ANSWERS 5. 8. 6. 57. 58. 7. 59. 60. 8
ANSWERS 66. Intersection at (, ) 69. Intersection at (, ) Solution 67. The lines are parallel; no solution. 70. Intersection at (,0) 68. Intersection (, ) 7. Intersection at (, 7) 9
76. 60 77. < 78. 60 79. $ 80..6 hours 8. 6.6 hours 8..7 hours 8. 00 mph 8. min. 85. 8 86. 0 ; 6 ; 88 0
GRAPH PAPER Introductory Algebra Final Exam Review